Question

Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is 4.22 × 108 m. Show that the mass of Jupiter is about one-thousandth that of the sun.​

Answer 1

Answer

Orbital period of I0 , TI0 = 1.769 days = 1.769 × 24 × 60 × 60 s

Orbital radius of I0 , RI0 = 4.22 × 108 m

Satellite I0 is revolving around the Jupiter

Mass of the latter is given by the relation:

MJ = 4π2RI03 / GTI02 .....(i)

Where,

MJ = Mass of Jupiter

G = Universal gravitational constant

Orbital period of the earth,

Te = 365.25 days = 365.25 × 24 × 60 × 60 s

Orbital radius of the Earth,

Re = 1 AU = 1.496 × 1011 m

Mass of sun is given as:

Ms = 4π2Re3 / GTe2 ......(ii)

∴ Ms / MJ = (4π2Re3 / GTe2) × (GTI02 / 4π2RI03) = (Re3 × TI02) / (RI03 × Te2)

Substituting the values, we get:

= (1.769 × 24 × 60 × 60 / 365.25 × 24 × 60 × 60)2 × (1.496 × 1011 / 4.22 × 108)3

= 1045.04

∴ Ms / MJ ~ 1000

Ms ~ 1000 × MJ

Hence, it can be inferred that the mass of Jupiter is about one-thousandth that of the Sun.

Answer 2

Answer:

Refer to the Attachment.

Hope it Helps !!!!